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A number $1$5 is divided into three parts which are in A.P. and the sum of their squares is $83$.

The highest part is:

  1. $3$
  2. $5$
  3. $6$
  4. $7$
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Let the $3$ numbers be $x-y , x , x+y$

Then, $x-y +x + x+y =15$

$\implies 3x= 15, x = 5$

Now put this value into their squares. $(5-y)^2 + 25 +( 5+y)^2 = 83$ and we get $y^2 = 4 \implies y = \pm 2.$

Hence, numbers are $5, 7,3 .$

And highest part is $7$
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